# cosh, coshf, coshl

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< c‎ | numeric‎ | math

Defined in header ``<math.h>`` |  |
float coshf( float arg ); | (1) | (since C99)
double cosh( double arg ); | (2) |
long double coshl( long double arg ); | (3) | (since C99)
Defined in header ``<tgmath.h>`` |  |
#define cosh( arg ) | (4) | (since C99)

1-3) Computes the hyperbolic cosine of `arg`.
4) Type-generic macro: If the argument has type long double, `coshl` is called. Otherwise, if the argument has integer type or the type double, `cosh` is called. Otherwise, `coshf` is called. If the argument is complex, then the macro invokes the corresponding complex function (ccoshf, ccosh, ccoshl).

### Parameters

arg | - | floating-point value representing a hyperbolic angle

### Return value

If no errors occur, the hyperbolic cosine of `arg` (cosh(arg), or

earg +e-arg
2

) is returned.

If a range error due to overflow occurs, +HUGE_VAL, `+HUGE_VALF`, or `+HUGE_VALL` is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is ±0, 1 is returned
- If the argument is ±∞, +∞ is returned
- if the argument is NaN, NaN is returned

### Notes

For the IEEE-compatible type double, if |arg| > 710.5, then `cosh(arg)` overflows.

### Example

Run this code

    #include <errno.h>
    #include <fenv.h>
    #include <math.h>
    #include <stdio.h>

    // #pragma STDC FENV_ACCESS ON
    int main(void)
    {
        printf("cosh(1) = %f\ncosh(-1)= %f\n", cosh(1), cosh(-1));
        printf("log(sinh(1) + cosh(1))=%f\n", log(sinh(1) + cosh(1)));
        // special values
        printf("cosh(+0) = %f\ncosh(-0) = %f\n", cosh(0.0), cosh(-0.0));
        // error handling
        errno = 0;
        feclearexcept(FE_ALL_EXCEPT);
        printf("cosh(710.5) = %f\n", cosh(710.5));
        if (errno == ERANGE)
            perror("    errno == ERANGE");
        if (fetestexcept(FE_OVERFLOW))
            puts("    FE_OVERFLOW raised");
    }

Possible output:

    cosh(1) = 1.543081
    cosh(-1)= 1.543081
    log(sinh(1) + cosh(1))=1.000000
    cosh(+0) = 1.000000
    cosh(-0) = 1.000000
    cosh(710.5) = inf
        errno == ERANGE: Numerical result out of range
        FE_OVERFLOW raised

### References

- C23 standard (ISO/IEC 9899:2024):

  - 7.12.5.4 The cosh functions (p: TBD)

  - 7.25 Type-generic math <tgmath.h> (p: TBD)

  - F.10.2.4 The cosh functions (p: TBD)

- C17 standard (ISO/IEC 9899:2018):

  - 7.12.5.4 The cosh functions (p: 176)

  - 7.25 Type-generic math <tgmath.h> (p: 272-273)

  - F.10.2.4 The cosh functions (p: 379)

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.5.4 The cosh functions (p: 241)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.2.4 The cosh functions (p: 520)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.5.4 The cosh functions (p: 222)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.2.4 The cosh functions (p: 457)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.3.1 The cosh function

### See also

sinhsinhfsinhl (C99)(C99) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
tanhtanhftanhl (C99)(C99) | computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function)
acoshacoshfacoshl (C99)(C99)(C99) | computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
ccoshccoshfccoshl (C99)(C99)(C99) | computes the complex hyperbolic cosine (function)
C++ documentation for cosh

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